Hawking Radiation in String Theory and the String Phase of Black Holes

Abstract

The quantum string emission by Black Holes is computed in the framework of the `string analogue model' (or thermodynamical approach), which is well suited to combine QFT and string theory in curved backgrounds (particulary here, as black holes and strings posses intrinsic thermal features and temperatures). The QFT-Hawking temperature T_H is upper bounded by the string temperature T_S in the black hole background. The black hole emission spectrum is an incomplete gamma function of (T_H - T_S). For T_H << T_S, it yields the QFT-Hawking emission. For T_H \to T_S, it shows highly massive string states dominate the emission and undergo a typical string phase transition to a microscopic `minimal' black hole of mass M_{\min} or radius r_{\min} (inversely proportional to T_S) and string temperature T_S. The semiclassical QFT black hole (of mass M and temperature T_H) and the string black hole (of mass M_{min} and temperature T_S) are mapped one into another by a `Dual' transform which links classical/QFT and quantum string regimes. The string back reaction effect (selfconsistent black hole solution of the semiclassical Einstein equations with mass M_+ (radius r_+) and temperature T_+) is computed. Both, the QFT and string black hole regimes are well defined and bounded: r_{min} leq r_+ \leq r_S, M_{min} \leq M_+ \leq M, T_H \leq T_+ \leq T_S. The string `minimal' black hole has a life time tau_{min} \simeq \frac{k_B c}{G \hbar} T^{-3}_S.